Metamaterials are artificially-structured resonant materials which manipulate the flow of electromagnetic energy to afford properties that are not typically found in naturally occurring materials. See V. G. Veselago, Soviet Physics Uspekhi-Ussr 10, 509 (1968); and R. A. Shelby et al., Science 292, 77 (2001). For example, electromagnetic cloaking has been demonstrated at microwave frequencies and it is theoretically plausible that the first perfect lens will be constructed entirely of negative refractive index metamaterials. See J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000); and D. Schurig et al., Science 314, 977 (2006). So far, most metamaterials have been fabricated using metallic unit cell structures embedded in a dielectric matrix. See T. J. Cui et al., in Metamaterials Theory, Design, and Applications, Springer, N.Y., 2010. Though well-suited for low frequency applications (e.g., <1 THz), metals are besieged by high ohmic losses at high frequencies which presents a tremendous challenge for implementing metamaterials that operate at optical frequencies (visible and infrared). See V. M. Shalaev et al., Opt. Lett. 30, 3356 (2005); S. Zhang et al, Phys. Rev. Lett. 95, 137404 (2005); G. Dolling et al., Opt. Lett. 31, 1800 (2006); G. Dolling et al., Opt. Lett. 32, 53 (2007); S. P. Burgos et al., Nat. Mater. 9, 407 (2010); C. M. Soukoulis et al., Science 315, 47 (2007); and V. M. Shalaev, Nat. Photonics 1, 41 (2007). Researchers have sought to compensate for ohmic loss with alternative strategies for reducing metamaterial absorption that include the development of gain media and protocols for fabricating 3D metamaterials supporting volumetric energy flow. See S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67 (2003); S. M. Xiao et al., Nature 466, 735 (2010); and D. B. Burckel et al., Adv. Mater. 22, 3171 (2010). One straight-forward way to drastically reduce metamaterial loss is to remove the metal completely and replace it with a very low loss dielectric resonator. See L. Lewin, Proc. Inst. Electr. Eng. 94, 65 (1947). In this case, the loss contribution of the dielectric matrix material begins to be appreciable compared to the low loss dielectric resonator.
The primary components of an all-dielectric metamaterial are two dielectric resonators which generate negative permittivity (−∈eff) and negative permeability (−μeff) simultaneously. See I. Vendik et al., Opto-Electron. Rev. 14, 179 (2006); Q. Zhao et al., Mater. Today 12, 60 (2009); C. L. Holloway et al., IEEE Trans. Antennas Propag. 51, 2596 (2003); Q. Zhao et al., Phys. Rev. Lett. 101 (2008); and J. C. Ginn et al., in OSA Technical Digest, Optical Society of America, Tuczon, Ariz., p. MWD2 (2010). At first glance, the importance of the dielectric matrix in these designs appears minimal; serving only as a support for the dielectric resonators. However, metamaterial fabrication is not trivial and the resonant fields of the dielectric resonators which extend into the dielectric matrix material must experience minimal attenuation. See D. J. Shelton et al., Nano Letters 11, 2104 (2011).
Therefore, a need remains for a matrix material that exhibits low loss at optical frequencies and facilitates the fabrication of all-dielectric metamaterials. Such a dielectric matrix material would be widely applicable to the fabrication of metal-dielectric metamaterials and a wide range of infrared optical devices as well.